To date, there have not been enough studies about the effects of curcumin against oxidative stress on sciatic nerves caused by streptozotocin (STZ) in diabetic rats. Therefore, this study was undertaken to determine whether curcumin, by virtue of its antioxidant properties, could affect the oxidant/antioxidant balance in the sciatic nerve and brain tissues of streptozotocin (STZ)-induced diabetic rats. A total of 28 rats were randomly divided into four groups of seven rats each: normal controls, only curcumin treated, diabetic controls, and diabetics treated with curcumin. Biomarkers—malondialdehyde (MDA), total oxidant status (TOS), total antioxidant status (TAS), oxidative stress index (OSI), and NO levels—for oxidative stress in the brain and sciatic nerve tissues of the rats were measured. We found a significant increase in MDA, NO, TOS, and OSI, along with a reduction in TAS levels in the brains and sciatic nerves of the STZ-induced diabetic rats (for both parameters p < 0.05). The MDA, TOS, OSI, and NO levels in these tissues were significantly reduced in the curcumin-treated diabetic group compared to the untreated diabetic group. In conclusion, the results of this study suggested that curcumin exhibits neuroprotective effects against oxidative damage in the brain and sciatic tissues of diabetic rats.